Wyniki 1-9 spośród 9 dla zapytania: authorDesc:"Bohdan MANDZIY"

Frequency Symbolic Analysis of Linear Periodically Time-Varying Circuits with Many Parametric Elements DOI:10.12915/pe.2014.05.013

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The possibility of application of frequency symbolic method of analysis of linear periodically time-varying (LPTV) circuits with one parametric element to the circuits with many parametric elements is shown. Such use requires the approximation of parametric transfer functions of circuit by Fourier series by the frequency of decomposition, that are equal to the greatest common divisor of basic frequencies of change parametric elements of circuit. Streszczenie. W artykule zaprezentowano możliwość zastosowania analizy częstotliwościowej w zadaniu wieloparametrowej identyfikacji usterek liniowych obwodów elektrycznych.Takie podejście wymaga wstępnego określenia transmitancji operatorowej obwodu przy wykorzystaniu szeregu Fouriera o częstotliwości bazowej równej największemu wspólnemu dzielnikowi podstawowej częstotliwości przy której zachodzą zmiany parametrów elementów obwodu. Wieloparametrowa analiza częstotliwościowa liniowych obwodów parametrycznych. Keywords: linear periodically time-variable circuits, frequency symbolic method. Słowakluczowe: liniowe obwody parametryczne, analiza częstotliwościowa. doi:10.12915/pe.2014.05.13 Introduction Most of parametric circuits that are used in electronic devices contains one parametric element [1]. Efficiency of functioning of such circuits may be achieved at significant depths of modulation of parameter of parametric element. However, increasing the depth of modulation, in practice, limited or can lead to the emergence unwanted harmonic components in the parameter of parametric element and, consequently in output signal. So sometimes it may be advisable introduction in circuit several parametric elements whose parameters vary in a relatively small limits. From the above follows and relevance of the proposed work. The formation of symbolic parametric transfer function W(s,t) of established mode of LPTV circuit with one parametric element that changes periodically in time with period T by f[...]

Mathematical model of linear parametric circuits relative to their external nodes

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The article deals with the matter of formation of differential equations of linear parametric circuits as a multipole. It also deals with two methods: exclusion of internal variables and their derivatives and also presenting differential equations to the necessary form relative to the external nodes of the multipole with the application of the certain matrix methods of variable exclusion. The algorithms and the examples of forming such models are presented. Streszczenie. W artykule zaprezentowano symboliczną metodę formułowania równań różniczkowych wielowrotnika o parametrach okresowo zmiennych w czasie. Równania wielowrotnika są wyznaczane na podstawie równań różniczkowych gałęzi obwodu. Zastosowano symboliczną macierzową metodę eliminacji zmiennych. Opracowano algorytm i zaprezento[...]

The peculiarities of analysis of linear parametric circuit performed by frequency-symbolic method

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The abstract deals with the methodology of symbolic analysis of linear parametric circuits in frequency field when the transfer function from the entrance of the circle to the parametric element is determined in the form of Furie truncated series. So, at a given outer signal parametric element is simulated by the sourse of additional signal. Then the circuit is analyzed by the classic method of analysis of linear circuits with constant parameters. Streszczenie: W pracy przedstawiono metodologię analizy symbolicznej obwodów w dziedzinie częstotliwości. Transmitancja obwodu o parametrach okresowo zmiennych czasie jest wyznaczana w postaci skończonego szeregu Fouriera. Element zmienny w czasie zostaje zastąpiony przez źródło sygnału. W wyniku dalsza analiza może być prowadzona tak jak d[...]

Peculiarities of frequency symbolic method applied to parametric circuits analysis

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The article deals with the assessment of asymptotic stability of linear parametric circuits by frequency symbolic method and approximation of transfer circuit function by the truncated Fourier series. Assessment of asymptotic stability is carried out according to the transfer function of one frequency. The examples of assessment of asymptomatic stability of single-circuit and double-circuit parametric amplifiers are given. Streszczenie. W artykule oceniono możliwość oszacowania asymptotycznej stabilności liniowych obwodów parametrycznych przy pomocy częstotliwościowej metody symbolicznej i aproksymacji transmitancji przez szereg Fouriera. Do oszacowanie asymptotycznej stabilności wykorzystywana jest zwyczajna transmitancja. Zaprezentowano przykład oszacowania stabilności jednooczkowego i dwooczkowego obwodu parametrycznego. (Osobliwości zastosowania metody symbolicznej do analizy obwodów parametrycznych) Keywords: symbolic analysis, linear parametric circuits, assessment of asymptotic stability. Słowa kluczowe: analiza symboliczna, parametryczne obwody liniowe, oszacowanie stabilności asymtotycznej. Introduction Linear parametric circuit of time t is characterized by impulse transfer function w(t, ) as a circuit response to delta-impulse given at the time period  . The function of two variables w(t, ) is often used. However, one variable is often considered as a parameter. At the same time the researcher should deal with so-called conjugate impulse reaction when the parameter is t or normal impulse reaction when the parameter is  [1]. This condition divides the sums of research of linear parametric circuits into two classes. So, the sums connected with the stability analysis in the supervision period [1] are done with the help of normal impulse reaction and their representations according to Laplace that are normal parametric transfer functions W(s, ) but the sums connected with the transfer of[...]

The Modified Frequency Symbolic Models (FSMs) of Linear Periodically Time-Variable Circuits

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The methods of constructing modified FSMs of linear periodically time-variable circuits represent systems of linear equations and not require special action for o account for harmonic signal components is considered. Filed modified FSMs of single-circuit parametric amplifier, which are formed by the discussed methods. Streszczenie. Artykuł omawia metody konstruowania zmodyfikowanych modeli FSMS liniowych obwodów opisanych układami równań liniowych i nie wymagających specjalnych działań dla uwzględnienia składowych harmonicznych sygnału. Zaprezentowano i omówiono przykładowy model zmodyfikowanego FSMS jedno-obwodowego wzmacniacza parametrycznego. (Zmodyfikowane modele częstotliwościowe liniowych obwodów okresowych). Keywords: linear parametric circuits, symbolic analysis, frequency symbolic models . Słowa kluczowe: liniowe obwody parametryczne, analiza symboliczna, częstotliwościowe modele symboliczne Introduction In [1] the formation of FSMs of a linear periodically timevariable (LPTV) circuit is considered. Each of such models are the system of linear algebraic equations (SLAE), and therefore can be analyzed by using analysis programs for the circuits with constant parameters. However, the mentioned FSMs have the general feature which consists that at calculations of time dependences of voltage or currents by such models it is necessary to carry out special actions that take into account the superposition of harmonic components of a signal [1]. In the proposed paper is presented a new, so-called, modified models of LPTV circuits which does not require implementation of specific actions are presented and are more simple in the further usage, for example, at the multivariate analysis. Technique The modified FSMs we build in the form of SLAE, therefore we can mark the following. As active elements of LPTV circuit (the resistors, controlled sources) are described by the algebraic component equations so a problem is creation of th[...]

Mathematical model for failure cause analysis of electrical systems with load-sharing redundancy of component

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In the paper, a mathematical reliability model for an electrical repairable system with parallel load-sharing redundancy of components is proposed. Such a model adequately accounts for the impact of load-sharing redundancy on cut set probability indexes. For reliability modelling, both dynamic fault tree and Markov analysis are used. Streszczenie. W artykule zaprezentowano model matematyczny system elektrycznego z równoległym obciążeniem i redundancją składowych obciążenia. Zastosowano analizę Markova i drzewo błędu dynamicznego. (Model matematyczny błędu w systemie elektrycznym powodowanego redundancją składowych obciążenia) Keywords: cut set, load-sharing redundancy, reliability model, dynamical fault tree, Markov model. Słowa kluczowe: model matematyczny, model Markova, drzewo błędu dynamicznego Introduction Recommendations to improve the reliability of technical systems are developed based on failure cause analysis. Each failure cause corresponds to a unique set of downstate components, which is called a cut. Accordingly, the purpose of reliability analysis is to determine all cuts, the content of each cut and the cut probability indexes. During such an analysis of a system with load-sharing redundancy of components, it is necessary to consider the impact of component failures on the upstate component load. Such an impact results in a change of the cut probability indexes. For consideration of these changes, it is necessary to suggest appropriate mathematical reliability models. This problem arises in providing reliability for electrical and power systems, which are used in high-risk applications. Literature review There are two different methods to determine the cut probability indexes: a logic and probabilistic approach and Markov analysis. The logic and probabilistic approach is based on the construction of logical conditions, which correspond to cuts. Furthermore, these logical conditions are transformed to appropriate[...]

The System Functions MAOPCs for Analysis and Optimization Of Linear Periodically Time-Variable Circuits Based on the Frequency Symbolic Method DOI:10.15199/48.2015.07.13

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In this paper we considered the following provisions: the architecture of system functions MAOPCs and examples of its application to solve tasks of multivariate analysis of LPTV circuits based on the frequency symbolic method. The method is based on approximation of transfer functions of LPTV circuits in the form of trigonometric polynomials of the Fourier. The system functions MAOPCs is implemented in the environment of MATLAB Streszczenie. W pracy zaprezentowano układ funkcji do symbolicznej analizy i optymalizacji obwodów parametrycznych, zmiennych w czasie. Metoda jest oparta na aproksymacji transmitancji obwodu parametrycznego za pomocą trygonometrycznego wielomianu Fouriera. Zaproponowany zbiór funkcji jest zaimplementowany w środowisku programu MATLAB. (Metoda symboliczna analizy i optymalizacji obwodów parametrycznych, zmiennych w czasie). Keywords: linear periodically time-variable circuits, frequency symbolic method, multivariate analysis, optimization. Słowa kluczowe: liniowe obwody parametryczne, wieloparametrowa analiza częstotliwościowa, optymalizacja. Introduction It is shown that [1,2,3] the frequency symbolic method (FS method) is an effective tool for the analysis of steady states of LPTV circuits in the frequency domain. The method is based on solving the equation of L.A. Zadeh [1] and the approximation of transfer function W( s,t ) ( s - complex variable, t - time) of LPTV circuit by trigonometric polynomial of the Fourier if some or all parameters of the circuit are defined by symbols [1]. This paper presents the architecture and application examples of system functions MAOPCs (Multivariate Analysis and Optimization of the Parametric Circuits) to solve tasks of multivariate analysis of LPTV circuits. The application of the system functions to solve the optimization tasks of linear parametric circuits, provided their stability control, are presented also in the papers [2,3]. The feature of the system MAOPCs lie[...]

The Effectiveness of Multivariate Computation of the Energy Characteristics of Linear Periodically-Time-Variable Circuits in the environment of MAOPCs DOI:10.15199/48.2017.10.27

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The ability of linear periodically-time-variable (LPTV) circuits to convert spectrum signals and perform parametric amplification of signals at low noise levels led to their important role in modern electronics. Over the past decade, the interest in LPTV circuits has significantly increased in connection with appearance of high-temperature superconductors and opportunities for their use in parametric amplifiers, high-Q resonators, filters, delay lines, etc. [1,2,3,4]. Modern software for circuit simulation of electronic circuits makes it possible to simulate the behavior of LPTV circuits usually in time domain, but does not provide a calculation of the functional characteristics of parametric nodes in steady state (frequency analysis). The most practical applicable method for LPTV circuits analysis in frequency domain, in our opinion, is the frequency symbolic method (FS-method) [5]. This method is based on using transfer functions of circuits that are represented in symbolic form, and allows us: a) calculate conjugate and normal parametric transfer functions [5,6] as approximate analytical expressions, the first of which connects the input and the output signals, second - contains information about the stability of the circuit; b)set the parameters of arbitrary elements circuit as symbols and calculate transfer functions of circuits in symbolic form; c) multiple times assign to those symbols the different values and explore their influence on the characteristics of the circuit. The confirmation of the foregoing is the system user-defined functions (UDF) MAOPCs (Multivariate Analysis and Optimization of the Parametric Circuits) [7], which are based on FS- method that is realized in a Matlab environment [8] and is intended for modeling, multivariate analysis and optimization of LPTV circuits in the frequency and time domains. By the FS-method, parametric transfer functions (conjugate and normal) of the circuit define approx[...]

Frequency symbolic models of linear parametric circuits

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The methods of constructing symbolic models of linear parametric circuits in frequency domain are considered. The models introduce the systems of linear algebraic equations . The circuit is considered to contain only one parametric element and in the model it is replaced with additional source of signal or frequency model of parametric element or controlled source. Frequency symbolic models of single-circuit parametric amplifier are formed according to the given methods. Streszczenie. Podano metodę tworzenia symbolicznego opisu obwodu liniowego zmiennego w czasie. Rozpatrzono obwód zawierający jeden kondensator zmienny w czasie. Kondensator jest zastępowany przez dodatkowe źródło starowane zależne od czasu i częstotliwości. Korzystając z opracowanej metody pokazano przykład modelowania wzmacniacza zawierającego kondensator zmienny w czasie. (Symboliczne modele częstotliwościowe obwodów zmiennych w czasie) Keywords: Linear parametric circuits, symbolic analysis, frequency symbolic models. Słowa kluczowe: Obwód zmienny w czasie, analiza symboliczna, model symboliczny w dziedzinie częstotliwości. Introduction Frequency symbolic method of analysis of linear parametric circuits with periodically variable parameters which allows for a known input signal X (s) using the parametric transfer function W(s,t) to determine the output signalY(s,t) in frequency domain is considered in [1] : (1) Y(s,t) W(s,t) X (s),    where s , t - complex variable and time variable, respectively. The approximation Wˆ (s, t) of parametric transfer functionW(s,t) is determined in the form of truncated Fourier series which contains k harmonic components. In this paper on the basis of frequency symbolic method the frequency symbolic models of parametric circuit are constructed and they represent the system of linear algebraic equations (SLAE) and they allow to conduct the further circuit analysis only in frequency domain. Three meth[...]

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